Small-scale clustering of Primordial Black Holes: cloud-in-cloud and exclusion effects

Abstract

Using an excursion-set approach, we revisit the initial spatial clustering of Primordial Black Holes (PBHs) originating from the Hubble re-entry of large Gaussian density fluctuations in the early universe. We derive the two-point correlation functions of PBHs, properly accounting for the "cloud-in-cloud" mechanism. Our expressions naturally and intrinsically correlate the formation of pairs of PBHs, which is a key difference with the Poisson model of clustering. Our approach effectively includes short-range exclusion effects and clarifies the clustering behaviors at small scale: PBHs are anti-correlated at short distances. Using a scale-independent collapse threshold, we derive explicit expressions for the excess probability to find pairs of PBHs separated by a distance $r$, as well as the excess probability to find pairs with asymmetric mass ratio. Our framework is model-independent by construction and we discuss possible other applications.

15 pages, 5 figures, matches published version

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Cited by in corpus (7)

• The Science of the Einstein Telescope
• Clustering of primordial black holes from quantum diffusion during inflation
• Constraints on primordial black holes for nonstandard cosmologies
• Clustering and Runaway Merging in a Primordial Black Hole Dominated Universe
• Projected gravitational wave constraints on primordial black hole abundance for extended mass distributions
• Primordial black holes with mass ratio-modulated initial clustering: merger suppression and projected constraints
• Excursion-set for Primordial Black Holes I: white noise and moving barrier